Washington -LRB- CNN -RRB- Republicans poised to take control of Congress are already threatening to kill what could turn out to be President Barack Obama 's most significant second-term achievement : a nuclear deal with Iran .

U.S. and Iranian negotiators are quickly approaching a November 24 deadline to reach an agreement that would freeze Iran 's nuclear program in return for lifting international sanctions on the Islamic Republic . Hopes for a deal have been rising , though Obama cautioned this weekend a `` big gap '' remains between the two sides and there are powerful constituencies in each country angling against an agreement .

In the United States , Republicans -- long skeptical of the talks -- are increasingly furious that Obama might sideline Congress to finalize an accord . They 're especially angry that the administration might make such a move after last week 's midterm elections gave the GOP -- dominated by foreign policy hard-liners -- firm control of the House and Senate .

`` Like North Korea in the 1990s , Iran will use a weak deal as cover to get nuclear weapons , '' said Illinois Republican Sen. Mark Kirk , a prominent skeptic of the negotiations .

Given the opposition , the Obama administration is believed to favor a framework agreement that , at least initially , would not require Congress to lift sanctions . Instead , the President would temporarily `` suspend '' them .

The personal stakes for Obama are immense as he seeks to restore his footing following last week 's election drubbing . A deal would elevate his legacy , which lacks a defining foreign policy triumph , and validate his vow to talk to leaders of U.S. enemies first made in a CNN campaign debate seven years ago .

It would also mark a stunning diplomatic breakthrough after 35 years of estrangement between Washington and Tehran and represent a major advance on one of the world 's thorniest non-proliferation problems .

Some of the president 's critics doubtless sense a chance to deny Obama a diplomatic win .

What to expect from the lame duck Congress

But others , including some Democrats , worry that Obama is being hoodwinked by Iran . They fear the mullahs will pocket sanctions relief and then cheat their way to a nuclear bomb .

Republicans could respond to what they see as a `` bad '' deal by seeking to impose new sanctions or drawing up punitive oversight benchmarks for Iranian compliance .

That could so sour already tenuous confidence between Washington and Tehran that the deal could crumble .

South Carolina GOP Sen. Lindsey Graham said this weekend that he would back a `` good '' Iran deal but would `` kill '' any agreement that he found problematic .

On Thursday , Graham will try to bring up a bill in the Senate that would require Obama to submit any agreement to Congress within three days for review . If he refuses , or if lawmakers vote to show their disapproval of the deal , funding for its implementation would be cutoff .

And Kirk has already pledged to mobilize the new Senate behind legislation he wrote with Democratic Sen. Robert Menendez which would target Iran 's oil industry with sanctions and provide a `` diplomatic insurance policy '' he says would result in a `` strong deal '' to reverse Tehran 's nuclear program .

Some Obama opponents on Capitol Hill reject the idea they are opposed to any deal and say an agreement is possible that would address their concerns . But they complain the White House has not worked with lawmakers to arrive at the best combination of carrots and sticks in the talks . They contend that a bad deal is now more likely because the administration has been too eager to make concessions to Iran .

The White House declined to discuss its tactics . But the administration has long warned that new sanctions would upend its diplomacy and it denies accusations that Obama plans to go around Congress .

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Obama would be sure veto any legislation that could threaten the agreement .

But Republicans could draw on skeptical Democrats to get closer to a veto proof majority of 67 Senate votes .

An official with a prominent pro-Israel policy group in Washington added : `` It is not a question of doing the math . The precise change is in the leader 's office . That now enables sanctions legislation to move forward . ''

But other sources doubt that if it really came to it , there would be enough Democrats to challenge the president 's veto and risk being accused of trashing a deal the rest of the world has embraced . But they admit the numbers are tightening .

Jim Walsh , a research associate at MIT and an expert on Iranian nuclear diplomacy , predicted a fierce political battle .

`` There will definitely be a fight . It will be a hard fight , but I think it will be a fight that the president can win because the consequences of failure are high , '' he said .

The White House has already won one skirmish over Iran .

Last year , critics sought to derail an interim nuclear deal , but failed largely because Democratic Senate Majority Leader Harry Reid blocked sanctions bills .

Obama will not have that safety net in the new Republican Senate that convenes in January , and backers of an agreement fear even the threat of tougher action .

Dylan Williams , director of government affairs for J Street , a left-leaning pro-Israel group said new sanctions would `` guarantee '' a fracturing of the international coalition against Iran .

Even if opponents fail to overcome a veto , Congress could still stir up the kind of trouble that could embolden hardline opponents of President Hassan Rouhani who argue Washington can never be trusted to stick to its commitments .

And a deal could not survive as `` temporary '' forever -- eventually Congress would have to act .

`` It is clear there is a significant problem , '' said Trita Parsi , founder of the National Iranian American Council , which advocates dialogue between Washington and Tehran . `` At the end of the day , the president needs to lift sanctions through Congress in order to make a deal possible . ''

The politics on Iran are getting trickier for Obama by the day .

Republicans are outraged at reports last week that he wrote to Iran 's Supreme Leader Ali Khamenei , days before the Ayatollah issued a barrage of tweets slamming the `` barbaric , wolflike and infanticidal regime '' in Israel .

Meanwhile , a report by the UN 's nuclear watchdog body last week suggested Tehran may have violated an interim nuclear deal by feeding natural uranium gas into one of its centrifuges . Iran was also accused of blocking existing inspections to its nuclear plants .

The White House has already shown it is ready to play political hardball over Iran , warning last year that anyone who opposes the deal is effectively backing a march to war with Iran .

Obama is also at odds over Iran with Israeli Prime minister Benjamin Netanyahu , who views the prospect of an Iranian bomb as an existential threat to the Jewish state . Netanyahu warned in a video address to Jewish Federations leaders on Tuesday that it was obvious Iran wanted to remove sanctions and it should be `` equally obvious '' that it is not prepared to dismantle its nuclear program in return .

The White House argues Israel 's demand for a complete dismantling of Iran 's nuclear infrastructure is impractical . Instead , it wants the deal between the permanent five members of the UN Security Council , Germany and Iran to lengthen the period of time it would take Tehran to dash towards a bomb .

`` We will not let Iran get a nuclear weapon . Period . We mean it , '' Vice President Joe Biden said in Washington Monday as negotiators from Iran , the US and Europe toiled in Oman to bridge gaps on a deal ahead of a final round of talks in Vienna next week .

In the event they 're successful , the pressure on key lawmakers from the White House and pro-Israel lobby groups will be intense .

Incoming Republican Senate Foreign Relations committee chairman Bob Corker will be a vital player , as he has voiced skepticism of the president 's Iran diplomacy in the past , while being more pragmatic than other Obama critics on sanctions .

Another key player is Sen. Chuck Schumer , who is staunchly pro-Israel but could give fellow Democrats cover to stick with their president by backing a deal .

And Hillary Clinton will increasingly be looked to by Democrats for guidance in the event of a deal . The former secretary of state and potential 2016 contender has backed Obama 's diplomacy but expressed skepticism Iran would sign on to a verifiable deal to halt its nuclear program.Â

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GOP senator to bring up bill that would require Obama to submit Iran deal for approval

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New sanctions could embolden hard-liners in Tehran

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White House likely to warn of possible march to war if agreement fails